Practicing Dialogue with 3 year olds

I'm teaching kindergartners in China, and am looking for ways to teach small dialogues to very small children - between 3 and 6.

For example:

Hello, what's your name?
My name is ...

I guess I didn't think it would be that difficult at first, but I've tried making a puppet to create a dialogue effect, and they didn't don't seem to grasp that well. They can barely say the sentence, "what's your name." They also just got name tags the today, so they really don't even know what their English names are yet, which complicates the dialogue even more.

Is dialogue a bit too much to ask from this age group? How can I make this work?

I had the same problem with my group. What I did was showing them a flashcard and elict the word, and they had to repeat it aloud three times. Don't expect children to respond very quickly, some take longer, some won't speak and some will speak a lot.
Don't give them long sentences. Stick to simple things like: I am Mary. Or: I like apples.
Once I did this activity that helped a lot: I was teaching emotions and colours, so I got hold of a bunch of different colored balloons and drew faces on them. Ss had to kick the balloon in the air and shout the color and emotion, for example: happy red balloon, sad yellow balloon, angry green balloon. It was lots of fun and they got a ton of practice.

3 year olds and dialogues hardly sounds like it should go together. I'd wonder though if there is some way you could introduce it as a song? Maybe it would get too complex but I'm thinking of something like 'row your boat' where it could be introduced with rounds even. Just throwing wild thoughts out there. Sorry if it's no real help.

Most of the time I'm just working on passive listening skills with this age group. They respond to English, sing some songs, practice single words, and answer questions. Getting them to perform simple conversations might be difficult, not impossible, just difficult

These all sound great. I hope I didn't make the dialogue thing sound too intense. It was mostly just trying to get them to say, "what's your name" and "I am blah."

I ended up doing thing where I bring in a paper bag filled with stuffed animals, sometime paper ones I made if I couldn't get any stuffed. The bag is a bit decorated, but the kids seem to really like the element of surprise. Then I say, "oh, look, my friends are in here. You have to say hello." They were way into this - it was awesome. So then my "friends" get nervous meeting new people, so the kids have to say, "what's your name?" so the animal will come out of the bag. Then one animal will come out, and I introduce it, and the kids repeat the "I am monkey, fish, whatever" part. This was super fun, and I could even do it sitting down! I'd even say, "oh, it's too loud, you're scaring my friends" and they hush up. It was a beautiful (quiet) teaching moment...

I brought in a colorful bag filled with "friends" - stuffed animals, and such. I would say, "oh, who's in here?" I'd then grab an animal, but just as it was coming out of the bag I'd put it back in and say, "he's scared!, we should say hello!" They were way into this. It was awesome. So then I say, "oh, he's still scared! Ask him, what's your name" And they do! After I introduce all of the animals, I "put them to sleep" by resting my head on my hands and making sleeping noises. By the time you finish up everyone is nice and quiet

It sounds like you got it going pretty well now. I'd still like to recommend the software from Genki English. Genki English has some great songs based around simple subjects in English that focus on building simple dialogue.

I'd recommend taking it slow. Look at the students' development in their native language. Sure, they are 3...but how are they progressing there? I wouldn't ask my students to do something they can't do in their own language. An example of this is pronunciation. There have been times when my students are saying words/sounds wrong. The parents get a bit upset and want me to correct it. I usually ask the students to say something in their own language that uses that sound. Sometimes, the pronunciation of that particular sound is wrong even in the native language. The parents then let up a little bit.

That said, just don't try to pressure them and give them fun Seems like you're doing that pretty well so far!

also, another great resource for songs, which is what I found my kids to learn quickly from, is dreamenglish.com where you can download the songs/videos (if you have realplayer). They LOVE these songs.